The invention relates to a method of determining a speed of rotation of a squirrel-cage motor and a computer software product according to the method. The speed of rotation is determined from an electric motor which is of a squirrel-cage motor type.
The invention relates to the determining of the rotation speed of squirrel-cage motors. The primary structural aspects determining the speed of rotation of a squirrel-cage motor are the pole pair number of the motor and the frequency of the voltage to be supplied to the motor. An unloaded squirrel-cage motor of a single pole pair rotates, in an ideal case, at a voltage frequency of 50 Hz at a synchronous speed of 3000 rotations per minute. If the number of pole pairs is increased, the synchronous speed of the motor decreases, whereby a motor rotation speed proportional to the pole pair number is arrived at by dividing 3000 rotations per minute by the number of the pole pairs of the squirrel-cage motor.
In other words, when there is no load on a squirrel-cage type motor, the motor rotates at a speed which is almost directly proportional to the frequency of the voltage supplying electric current to the motor, i.e. synchronous speed. The rotation speed of the squirrel-cage motor deviates downward from the synchronous speed by the amount of the motor slip, the rotation speed of the motor being lower than the synchronous speed proportioned to voltage frequency by the amount of the slip.
The rotation speed of a squirrel-cage motor is also proportional to the motor load. As the load on the motor increases, its rotation speed begins to decrease. The motor torque rises steeply, in accordance with the squirrel-cage motor torque curve, up to the point of maximum torque after which the torque starts to decrease again, whereby the load on the motor grows so great that the motor begins to slip from the speed provided by the voltage frequency of the current supply system. FIG. 2 shows the torque curve of a squirrel-cage motor.
Due to the above described phenomenon, the precise instantaneous speed of rotation depends on several factors, i.e. the structure, slip and load of the motor, and the frequency of the voltage supplied to the motor.
In prior art measurement solutions, rotation speed of motors is measured using tachometer or stroboscope measurements. There are, however, major drawbacks in the prior art. When a tachometer is used for measuring speed of rotation, there must be one mounted in the motor, or one must be mounted for the measurement. Correspondingly, when a stroboscope is used, the motor must contain the means for carrying out the measurement. Motors do not usually have built-in speed measurement devices, but the motor must be halted for mounting one. However, motors used in industrial processes cannot usually be halted without causing undue harm for the process of which the motor is a part. In addition, a squirrel cage motor used in an industrial process may be located in a space where the mounting of the measurement device is difficult, or almost impossible. As an example, a gaseous space or one where there is a risk of an explosion could be mentioned.
It is also known in the art to measure the current taken by a motor with an ammeter. The measurement can be carried out by connecting an ammeter coupled to a data collection means, such as a PC, to a wire that supplies electric current to the motor, the measurement being then carried out by collecting samples from the current taken by the motor. The measurement data obtained from the meter is stored in the memory of the data collection means and processed using software which produces a spectrum of the measurement data for visual analysis. This method of determining requires a discrete Fourier analysis (DFT) of the signal. In DFT, the measurement time and the frequency resolution (the distinction between two consecutive frequency points) are interrelated in that the better the desired resolution, the longer is the measurement time required. A long measurement time is a problem, because the motor load, and thereby its speed of rotation, should remain constant during the measurement to allow accurate and reliable measurement data to be collected. When the motor is used in an industrial process, this is not, however, usually possible without causing undue harm for the process. Secondly, in the DFT method the set of frequency points where the calculation is to be carried out is determined in advance by the measurement time and the sampling frequency. If the speed of rotation is not exactly the same as the frequency of any of the frequency points, error will occur in the estimation of fault frequencies, which are proportional to the speed of rotation, and, consequently, amplitude estimate will also be erroneous.
The precise instantaneous rotation speed of the squirrel-cage motor depends on several factors, i.e. on the structure, slip and load of the motor, and the frequency of the voltage supplied to the motor. As illustrated above, drawbacks that often appear in connection with the prior art is the need to halt the motor for the mounting of the speed measurement device, the need for a plural number of measurement devices and, thereby, the need to carry out various measurements to allow an analysis to be made. Moreover, an accurate analysis requires a long measurement time, during which a constant speed of rotation of the motor is required. This naturally slows down and complicates the measurement, and impairs its accuracy and reliability.
It is an object of the invention to alleviate the drawbacks of the prior art and to provide an improved method of determining speed of rotation, and computer software implementing the method.
This is achieved by a method and computer software of the present invention comprising the characteristics set forth in the claims.
An underlying idea of the invention is that the speed of rotation of a squirrel-cage motor is determined by measuring, with an ammeter suitable for the purpose, electric current from one phase supplying power to the motor. From the electric current taken by the squirrel-cage motor is collected measurement data at a suitable sampling frequency for a predetermined measurement period. The measurement data is stored in the memory of a data carrier as measurement data of a fixed format from which the rotation speed of the squirrel-cage motor can be estimated by calculation, the electric current taken by the squirrel-cage motor being proportional to the speed of rotation of the motor such that the motor takes the highest current at a frequency corresponding to the base frequency, and a side frequency lower than the base frequency by the rotation frequency and a side frequency higher than the base frequency by the rotation frequency show clearly distinguishable current values, and by determining the frequencies at which they appear, the actual rotation speed of the squirrel-cage motor can be determined by subtracting the lower side frequency from the higher side frequency and by dividing the difference thus obtained by two which allows to determine the instantaneous rotation speed of the squirrel-cage motor. These side frequencies proportional to the pole pair number are estimated from the measurement data using a maximum likelihood estimate (MLE) which is calculated by maximizing the maximum likelihood function (MLF) of the measurement data. The side frequencies proportional to the pole pair number are found at frequency points where the maximum likelihood function (MLF) obtains its highest values.
Before the ML function is calculated to find the side frequencies proportional to the pole pair number, a base frequency is estimated from the measurement data, the estimation being also carried out using the maximum likelihood estimate (MLE) calculated by maximizing the maximum likelihood function (MLF) of the measurement data. The base frequency is found at a frequency point where the maximum likelihood function (MLF) obtains its highest value. Next, a sine signal of the base frequency is generated, the signal having the same amplitude and phase as the base frequency current taken by the squirrel-cage motor from the electric supply network. The signal thus generated is subtracted from the measurement data to provide a more accurate estimation of the frequencies proportional to the pole pair number.
The speed of rotation is determined using the maximum likelihood estimate of the time domain. This provides an advantage in that the measurement time needed for determining the frequency is now significantly shorter than in the conventional DFT method. The reason for this is that in the maximum likelihood method, frequency is produced as a continuous variable and not as separate values in which the minimum difference between two frequency values, i.e. their resolution, is determined by the measurement time and the sampling frequency, as in the commonly used DFT method of the frequency domain. In the maximum likelihood method the only factor having an effect on the accuracy at which the speed of rotation can be determined is the magnitude of interference in the measurement signal.
Practice has shown that for the impact of the interference that is in the measurement signals to be eliminated, the length of the measurement period must be more than 100 times the cycle length of the basic current and voltage frequency. The measurement time is, however, advantageously short in proportion to the variation in the speed of rotation caused by variations in the motor load. For example, at a basic current and voltage frequency of 50 Hz, the required measurement time is 2 seconds in the maximum likelihood method, whereas in DFT methods a measurement time of about 30 seconds is needed to obtain the required resolution.
For sufficiently reliable measurement results, a sampling frequency about three times the highest frequency to be estimated is preferred, i.e. the base frequency with the speed of rotation added thereto.
An advantage of the described method of determining the speed of a squirrel-cage motor is that there is no need to know the shape of the torque curve of the squirrel-cage motor or other parameters relating to it. It suffices to know the pole pair number of the motor and the frequency of the current taken by the motor.
A further advantage is that no speed measuring devices need to be installed to the motor, which produces costs savings. In addition, the collection of the measurement data needed for the speed measurement can be carried out in a central unit feeding the motor, which provides another advantage in that there is no need to enter the motor space or to have separate wiring, but the measurements of even a plural number of motors can be carried out in a centralized manner in one and the same motor feeding central unit. Moreover, this enables the speed measurement method to be used advantageously in connection with a real-time, centralized control and monitoring system.